sha1_base64="U94f3z6l97Xyl6EofN8Tlv7UmvY=">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</latexit> > 0 <latexit sha1_base64="nTN0VlqjikVD87chh4w6hftdmaA=">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</latexit> L(w) = 1 n n X i=1 `(hw, yixi i) <latexit sha1_base64="HT//l12ddZJZk79nPIE4VHhdBgA=">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</latexit> `(z) = log(1 + exp( z)) <latexit sha1_base64="CARv2nJ+nhBeOVEQJmaph73E5fs=">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</latexit> dw(t) dt = rL(w(t)) " Soudry, D., Hoffer, E., Nacson, M., Gunasekar, S., & Srebro, N. (2018). The implicit bias of gradient descent on separable data. ( ) : <latexit sha1_base64="YLv0/ozj2evA7J6/U7CrSd67fOY=">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</latexit> w(t) = ˆ w log t + ⇢(t) <latexit sha1_base64="Zw/0V8Yw0bx42w0Ht/geiS1KiM0=">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</latexit> ˆ w <latexit sha1_base64="BlYTNRSSw5Mn+3FsC7sLJk53Ec4=">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</latexit> minw2Rd kwk2 s.t. 8i : hw, yixi i 1 <latexit sha1_base64="DOiigtDB2ez37UFZCYyJ9z27RNA=">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</latexit> ⇢(t)